The acceleration of Method-of-Moment (MoM) calculations often relies on compression of blocks of the MoM impedance matrix. This can be carried out algebraically, operating exclusively on lines and columns of the matrix. Here, we focus on physically-based compression techniques. Approaches based on multipole decompositions and on complex plane wave expansions are compared from the perspective of the rank of the interaction matrix and its dependence on distance. A drawback of the complex plane-wave expansion is mitigated by defining a set of patterns that can be reused when computing interactions between any pair of blocks.